Discrete Mathematics and Graphs

Czech Technical University in Prague
Faculty of Electrical Engineering
Bachelor Degree in Electrical Engineering and Computer Science
Academic Year 2019/2020

Announcements:

  • If you want to take the oral exam, you can choose one of the dates below. Contact me by email to fix it.
  • You can find the results of the Midterm here.

Information on the Exams:

  • Exam Modalities.
  • The exam period will be from January 13 to February 16, 2020.
  • There will be 5 written exams in the exam period:

    • Thursday 9 January, from 14:00 to 16:00 in classroom JP:B3-515
    • Monday 20 January, from 9:00 to 11:00 in classroom T2:C3-51
    • Thursday 23 January, from 9:00 to 11:00 in classroom T2:C3-51
    • Wednesday 05 February, from 9:00 to 11:00 in classroom T2:C3-51
    • Monday 10 February, from 9:00 to 11:00 in classroom T2:C3-51
  • Dates for the (non mandatory) oral exam:

    • 10 January, from 14:00 in classroom JP:B3-515
    • 21 January, from 14:00 in classroom JP:B3-515
    • 24 January, from 14:00 in classroom JP:B3-515
    • 06 February, from 14:00 in classroom JP:B3-515
    • 11 February, from 14:00 in classroom JP:B3-515
    • 14 February, from 14:00 in classroom JP:B3-515

Contents and Materials:

Many thanks to Prof. Marie Demlova for generously sharing her notes with us.
  1. Chapter 1. Logic
    Propositional logic, predicate logic, quantifiers, interpretation.
    Materials: Lect1, Ex1, Lect2, Ex2.
  2. Chapter 2. Sets
    Functions, operations on sets, equivalence relations, partial orders, combinatorics, Pascal's triangle, countable and uncountable sets.
    Materials: Lect3, Ex3, Lect4, Ex4, Lect5, Ex5.
  3. Chapter 3. Arithmetic
    Euclid algorithms, Diophantine equations, relation modulo n, operations on Zn.
    Materials: Lect6, Ex6, Lect7, Ex7.
  4. Chapter 4. Algebraic structures
    Semigroups, groups, Lagrange theorem, order of an element, the Euler function, rings and fields.
    Materials: Lect8, Ex8, Lect9, Ex9, Lect10, Ex10, Syllabus.
  5. Chapter 5. Graphs
    Graphs and directed graphs, walks, reachable vertices, Euler and Hamiltonian graphs, strong connectivity, spanning trees.
    Materials: Lect11, Ex11, Lect12, Ex12, Lect13, Ex13, Syllabus.
Below you may find a sample of exams:

References:

  • L.N. Childs, A Concrete Introduction to Higher Algebra, Springer.
  • R. Johnsonbaugh, Discrete Mathematics, Prentice Hall.
Responsible person: doc. RNDr. Martin Bohata, Ph.D.